New estimation algorithms for discrete non-linear systems and observations with multiple time delays

Abstract

This paper derives new estimation algorithms for discrete non-linear systems and observations with multiple time delays. The results directly yield the fixed-interval, fixed-lag, fixed-point smoothing and the filtering algorithms. The derivation makes use of the matrix minimum principle to minimize the error variance, taken to be the estimation criterion. For systems with polynomial or product type non-linearities, the algorithms are physically realizable, under the assumption that the conditional probability density functions of the estimator errors are Gaussian. Examples illustrating the use of the algorithms are presented.